CPT and Lorentz Symmetry

The following sections are included:

• Preface
• Contents

We report bounds from a second generation LLI violation experiment using Hg and Cs magnetometers. The experiment is mounted on a rotating table that has made it possible to reduce experimental noise and to extract the first bounds on for the proton and neutron. The same experiment can be used in conjunction with a polarized electron spin map of the Earth to place bounds on long range spin-spin interactions. For some of the proposed long-range spin-spin interactions, these new bounds are a million times more restrictive than the bounds derived by other methods. Our upper bound on the magnitude of the spin-spin force between an electron and a neutron is nearly a million times smaller than their gravitational attraction.

Studying fundamental symmetries of Nature has proven fruitful in particle physics. I argue that recent results at the LHC, and the naturalness problem highlighted by them, provide a renewed motivation for tests of CPT symmetry as a probe for physics beyond quantum field theory. I also discuss prospects for antihydrogen CPT tests with sensitivities to Planck scale suppressed effects.

The Double Chooz reactor-based oscillation experiment searches for an electron antineutrino disappearance signal to investigate the neutrino mass matrix mixing angle θ₁₃. Double Chooz's reported evidence for this disappearance is generally interpreted as mass-driven mixing through this parameter. However, the electron antineutrino candidates collected by the experiment can also be used to search for a signature of the violation of Lorentz invariance. We study the sidereal time dependence of the antineutrino signal rate and probe Lorentz violation within the Standard-Model Extension (SME) framework. We find that the data prefer the sidereal time independent solution, and a number of limits are applied to the relevant SME coefficients, including the first constraints on those associated with Lorentz violation in the e-τ mixing sector.

Galileo Galilei (GG) is a small satellite to fly in a low altitude, near circular, Sun-synchronous orbit around the Earth with the goal of testing in its field the weak equivalence principle to 10⁻¹⁷. It would improve the best tests with slowly rotating torsion balances by four orders of magnitude. The sensor is a differential accelerometer with two concentric coaxial test cylinders of different composition rotating together with the whole satellite around the symmetry axis, and weakly coupled in the plane perpendicular to it as a 2D mechanical oscillator. One axis rotation at 1 Hz, to be provided once and for all at launch, stabilizes the satellite and up-converts the signal from the low orbital frequency of ≃1.7 · 10⁻⁴ Hz to the much higher 1 Hz rotation frequency, needing neither motor nor bearings (passive rotation). For test masses suspended in orbit the major gain is a signal from Earth almost 500 times stronger than for the same masses suspended on ground. In GG both the sensor and the spacecraft are designed to fully exploit the properties of space in order to push the test four orders of magnitude better than slowly rotating torsion balances on ground.

The comparison of the free precession of co-located ³He-¹²⁹Xe spins (clock comparison) enables us to search for very tiny nonmagnetic spin interactions. With our setup we could establish new limits for Lorentz invariance violating interactions of spins with a relic background field which permeates the Universe and points in a preferred direction in space.

I review some of the major developments in the theoretical background and experimental uses of binary pulsars to explore local Lorentz invariance in the gravitational sector and its possible violation.

Lorentz invariance violation (LIV) in the weak interaction is studied, both experimentally and theoretically, at the Kernfysisch Versneller Instituut. Here, it is discussed which new observables can be measured, and which experimental methods can be used. An outlook towards high statistics experiments is given.

MAGIC is a gamma-ray telescope system located on the Canary Island of La Palma. With it, the northern very-high energy (VHE) gamma-ray sky can be observed at >50 GeV, bridging the gap in energy between satellite and ground-based measurements. In this overview, we particularly highlight source classes whose VHE gamma-ray observations bear potential of contributing to Lorentz invariance tests: pulsars, active galactic nuclei, and gamma-ray bursts.

This contribution to the CPT'13 meeting briefly introduces Lorentz and CPT violation and outlines two recent developments in the field.

The frequencies of Cs and Rb fountain clocks have been compared to various H-masers to search for periodic changes correlated with the gravitational potential and boost with respect to the cosmic microwave background. The data span about eight years and the main sources of long-term noise are the offsets and linear drifts associated with the H-masers. To circumvent these effects we apply a numerical derivative to the data, which significantly reduces the standard error. We determine a limit for the Local Position Invariance (LPI) coefficient with respect to gravity to be 4.8×10⁻⁶ and 10⁻⁵ for a Cs-H and Rb-H comparison, respectively. From the same data the boost LPI coefficients were measured to parts in 10¹¹. From these results and others, independent limits on all coefficients of the boost violation vector with respect to fundamental constant invariance were determined to parts in 10¹⁰.

Dehmelt and VanDyck's famous 1987 measurement of the electron and positron g-factor is still the most precise g-factor comparison in the lepton sector, and a sensitive test of possible CPT violation. A complementary g-factor comparison between the proton and the antiproton is highly desirable to test CPT symmetry in the baryon sector. Current experiments, based on Dehmelt's continuous Stern-Gerlach effect and the double Penning-trap technique, are making rapid progress. They are, however, extremely difficult to carry out because ground state cooling using cryogenic techniques is virtually impossible for heavy baryons, and because the continous Stern-Gerlach effect scales as μ/m, where m is the mass of the particle and μ its magnetic moment. Both difficulties will ultimately limit the accuracy. We discuss experimental prospects of realizing an alternative approach to a g-factor comparison with single (anti)protons, based on quantum logic techniques proposed by Heinzen and Wineland and by Wineland et al. The basic idea is to cool, control and measure single (anti)protons through interaction with a well-controlled atomic ion.

X-ray and gamma-ray observations of astrophysical objects at cosmological distances can be used to probe the energy dependence of the speed of light with high accuracy and to search for violations of Lorentz invariance and CPT symmetry at the Planck energy scale. In this conference contribution, we discuss these searches in the theoretical framework of the Standard-Model Extension. We present new limits on the dispersion relation governed by operators of mass dimension d = 5 and d = 6, and we discuss avenues for future progress.

We propose using a Stark interference technique to measure directly the odd-parity c_0j components of the electron sector c_μν tensor of the Standard-Model Extension. This technique has been shown to be a sensitive probe of parity violation in atomic dysprosium in a low-energy, tabletop experiment, and may also be straightforwardly applied to test Lorentz invariance. We estimate that such an experiment may be sensitive to c_0j coefficients as small as 10^−18;.

Searches for Lorentz and CPT violation using neutrino oscillations and the prospects for future tests using neutrino time-of-flight measurements and beta-decay experiments are presented.

We searched for a sidereal modulation in the rate of neutrinos observed by the MINOS Far Detector. The detection of these signals could be a signature of neutrino-antineutrino mixing due to Lorentz and CPT violation as described by the Standard-Model Extension framework. We found no evidence for these sidereal signals and we placed limits on the coefficients in this theory describing the effect.

The equivalence principle can be tested by precision experiments based on classical and quantum systems, on the ground as well as in space. In many models, these tests are mostly equivalent in their ability to constrain physics beyond the Standard Model. We mention differences that nevertheless exist between spaceborne and quantum mechanical tests and their conventional competitors.

This brief review discusses Lorentz-violating operators of arbitrary dimension within the photon and neutrino sectors of the Standard-Model Extension.

After the first production of cold antihydrogen about ten years ago, second-generation experiments whose aim it is to measure the fundamental properties of this anti-atom are beginning to become operational. The AEGIS experiment will test the weak equivalence principle of General Relativity by measuring the gravitational interaction between matter and antimatter with the help of a pulsed, cold antihydrogen beam. The vertical deflection of antihydrogen atoms in the gravitational field of the Earth will be determined with a moiré deflectometer. In the present paper, the principle of the experiment will be reviewed and its present status will be presented.

High-energy astrophysics observations provide the best possibilities to detect a very small violation of Lorentz invariance, such as may be related to the structure of spacetime near the Planck scale. I will discuss the possible signatures of Lorentz invariance violation that can be manifested by observing the spectra, polarization, and timing of γ-rays from active galactic nuclei and γ-ray bursts. Other sensitive tests are provided by observations of the spectra of ultrahighenergy cosmic rays and very high-energy neutrinos. I will also discuss a new time-of-flight analysis of observations of GRB 090510 by the Fermi γ-ray Space Telescope. These results, based on high-energy astrophysical observations, have fundamental implications for spacetime physics and quantum gravity models.

The KATRIN experiment, presently under construction in Karlsruhe, Germany, will improve on previous laboratory limits on the neutrino mass by a factor of ten. KATRIN will use a high-activity, gaseous T₂ source and a very high-resolution spectrometer to measure the shape of the high-energy tail of the tritium-decay β spectrum. The shape measurement will also be sensitive to new physics, including sterile neutrinos and Lorentz violation. This report summarizes recent progress in the experiment.

Constraints on Lorentz violation in matter-gravity couplings are summarized along with existing proposals to obtain sensitivities that exceed current limits by up to 11 orders of magnitude.

We have studied the effect of hypothetical violations of Lorentz and CPT symmetry by calculating the corrections to the energy levels of hydrogen induced by the Standard-Model Extension (SME). Hydrogen studies are interesting because the energy levels of hydrogen can be measured with great precision and the theory for hydrogen based on the Standard Model (SM) is well understood. We obtained corrections through order α² times the SME parameters for all levels of hydrogen and applied them to determine the SME corrections to the transition frequency for the 2S-1S transition.

The Space-Time Explorer and Quantum Equivalence Space Test (STEQUEST) satellite mission is devoted to testing several aspects of General Relativity using an atomic clock and a differential dual-species atom interferometer in space. The latter aims at performing a quantum test of the Einstein equivalence principle in the perigee phase of a highly elliptical Earth orbit by probing the universality of free fall with coherent matter waves. In this paper, we give a brief summary on the mission and the prospects for the dual-species atom interferometer.

Atomic spin comagnetometers are among the most sensitive devices for testing Lorentz symmetry of fermions. In Princeton, we have used our rotating comagnetometer to set the most stringent limits on CPT-odd and CPT-even Lorentz violating effects in neutrons. However, gyroscopic pickup of the Earth's rotation represents a significant systematic effect limiting sensitivity. To suppress this systematic, we have installed a Rb-²¹Ne comagnetometer at the Amundsen-Scott South Pole Station with data collection being performed over the course of the austral winter.

This talk, given at CPT'13, showed Super-Kamiokande atmospheric-neutrino Monte Carlo sensitivity to Lorentz-violation effects using the perturbative model derived from the Standard-Model Extension.

The KLOE experiment at the DAΦNE ϕ-factory of the INFN Frascati Laboratory collected data corresponding to 2.5 fb⁻¹ of integrated luminosity. A new approach to the analysis of ϕ → K_S K_L → π⁺π⁻, π⁺π⁻ events has been adopted allowing us to independently measure all four CPT violating parameters Δ_aμ appearing for neutral kaons in the SME. The final KLOE results on Δ_aμ are presented: Δ_a0 = (−6.0 ± 7.7_stat ± 3.1_syst) × 10⁻¹⁸ GeV, Δ_aX = (0.9 ± 1.5_stat ± 0.6_syst) × 10⁻¹⁸ GeV, Δ_aY = (−2.0 ± 1.5_stat ± 0.5_syst) × 10⁻¹⁸ GeV, Δ_aZ = (3.1 ± 1.7_stat ± 0.5_syst) × 10⁻¹⁸ GeV. The KLOE-2 experiment is going to start a new data taking campaign at DAΦNE upgraded in luminosity, allowing to reach a sensitivity of GeV for all Δ_aμ parameters.

In this communication, we focus on possibilities to constrain SME coefficients using Cassini and Messenger data. We present simulations of radioscience observables within the framework of the SME, identify the linear combinations of SME coefficients the observations depend on and determine the sensitivity of these measurements to the SME coefficients. We show that these datasets are very powerful for constraining SME coefficients.

The MINOS experiment uses two neutrino detectors separated by 735 km. Two measurements of the neutrino time of flight were conducted between the two detectors. The first analysis uses the statistics accumulated during 7 years of data taking. The second analysis was done using the data collected during 2012 making use of a new system of clocks which provided a more precise measurement of time at the primary proton target, the Near and the Far Detectors. Using the resulting neutrino time of flight between the MINOS detectors we present an improved neutrino velocity measurement.

The concept and prospects of a proposed international network of geographically separated, time-synchronized ultrasensitive atomic comagnetometers to search for correlated transient signals heralding new physics is discussed. The Global Network of Optical Magnetometers for Exotic physics (GNOME) would be sensitive to nuclear and electron spin couplings to various exotic fields. To date, no such search has ever been carried out, making the GNOME a novel experimental window on new physics.

Perturbative calculations in quantum field theory often require the regularization of infrared divergences. In quantum electrodynamics, such a regularization can for example be accomplished by a photon mass introduced via the Stueckelberg method. The present work extends this method to the QED limit of the Lorentz- and CPT-violating Standard-Model Extension.

The Sounding-Rocket Principle Of Equivalence Measurement (SR-POEM) will test the weak equivalence principle (WEP) to 2 × 10⁻¹⁷ g in an experiment launched into free fall by a sounding rocket. The high sensitivity is possible in a short time because: (1) our laser distance gauges measure to 0.1 pm in 1 second; (2) the high measurement speed allows us to keep the temperature of the critical region stable to within a few μK using two cascaded thermal low-pass filters; (3) the spacing between the physics package and the test masses is kept constant by virtue of a servo (but not a drag-free satellite); (4) the test masses (TMs) are unconstrained during drops, avoiding constraint-force imperfections; and (5) the position measurement is to a plate that is almost stationary with respect to the TMs (by virtue of the position servo and the initialization of the TMs).

The Gupta-Bleuler quantization procedure is applied to the SME photon sector. A direct application of the method to the massless case fails due to an unavoidable incompleteness in the polarization states. A mass term can be included into the photon lagrangian to rescue the quantization procedure and maintain covariance.

Microwave cavities can be used to generate signals that exhibit fractional frequency stabilities on the order of parts in 10⁻¹⁶. Such signals provide an excellent tool for constraining potential violations of local Lorentz invariance in the photon sector of the Standard-Model Extension. In this work we describe the current methods employed to design and construct such an experiment.

We report some general phenomenological results concerning CP and CPT violations in joint decays of entangled pseudoscalar neutral mesons.

We propose a CPT-even and Lorentz-violating dimension-five nonminimal coupling between fermionic and gauge fields, involving the CPT-even and Lorentz-violating gauge tensor of the Standard-Model Extension. This nonminimal coupling modifies the nonrelativistic regime of Dirac particles, inducing new effects such as an electric-Zeeman-like spectrum splitting and an anomalous-like contribution to the electron magnetic moment. These new effects allow to constrain the magnitude of this nonminimal coupling in 1 part in 10¹⁶.

We present the design and first measurement results for an ultra-stable cryogenically cooled optical sapphire resonator system with a potential relative frequency stability better than 3 × 10⁻¹⁷. This level of oscillator stability allows for more precise tests of Einstein's theories of relativity and thus could help to find first hints of new physics. We will give some details on a projected experiment to test Lorentz invariance that will utilize these cavities.

OPERA's claim to have seen faster-than-light neutrinos made a big splash in 2011. However, indirect arguments, based on gauge invariance, phase coherence in neutrino oscillations, and observations of electrons, could have already been used to rule out the OPERA claim. In fact, indirect constraints on neutrino velocities are many orders of magnitude better than direct ones.

Gravitational theories with Lorentz violation must account for a number of possible features in order to be consistent theoretically and phenomenologically. A brief summary of these features is given here. They include evasion of a no-go theorem, connections between spontaneous Lorentz breaking and diffeomorphism breaking, the appearance of massless Nambu-Goldstone modes and massive Higgs modes, and the possibility of a Higgs mechanism in gravity.

Lorentz and CPT violation can affect the rates for production and decay. The Lorentz-violating coefficients in the Standard-Model Extension responsible for modifying the top-quark events have recently been bounded by the D0 Collaboration. To extend the analysis to the LHC the calculations need to be extended to include the gluon fusion production mechanism. Some of the first results of this program were presented at the Meeting.

A DØ analysis measuring the charge asymmetry A^b_sl of like-sign dimuon events due to semileptonic b-hadron decays at the Fermilab Tevatron Collider has shown indications of possible anomalous CP violation in the mixing of neutral B mesons. This result has been used to extract the first senstivity to CPT violation in the B⁰_s system. An analysis to explore further this anomaly by specifically measuring the semileptonic charge asymmetry, a^s_sl, in B⁰_s decays is described, as well as how a variant of this analysis can be used to explore a larger set of CPT-violating parameters in the B⁰_s system for the first time.

We consider the possibility of Lorentz-invariance violation in weak-decay processes. We present a general approach that entails modifying the W-boson propagator by adding a Lorentz-violating tensor to it. We describe the effects of Lorentz violation on nuclear β decay in this scenario. In particular we show the expression for a first-forbidden transition with a spin change of two. Using data from an old experiment on the rotational invariance of yttrium-90, we derive several bounds on the Lorentz-violating parameters of the order of 10⁻⁶-10⁻⁸.

The physics of classical particles in a Lorentz-breaking spacetime has numerous features resembling the properties of Finsler geometry. In particular, the Lagrange function plays a role similar to that of a Finsler structure function. A summary is presented of recent results, including new calculable Finsler structures based on Lagrange functions appearing in the Lorentz-violation framework known as the Standard-Model Extension.

We present a method to calculate the nonrelativistic hamiltonian for the minimal Standard-Model Extension matter sector in a uniform gravitational field. The resulting hamiltonian coincides with earlier results in the corresponding limits but it also includes spin-dependent terms that were previously unknown. The phenomenology associated with this hamiltonian is briefly discussed.

This article reviews the methods used to obtain a two-sided bound on isotropic modified Maxwell theory from experimental data of ultra high-energy cosmic rays in 2008. The bound is updated with results from the HEGRA experiment.

We give a brief overview of time dilation tests using high-resolution laser spectroscopy at heavy-ion storage rings. We reflect on the various methods used to eliminate the first-order Doppler effect and on the pitfalls encountered, and comment on possible extensions at future facilities providing relativistic heavy ion beams at γ ≫ 1.

The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.

We use the final results from Gravity Probe B to set new upper limits on the gravitational sector of the Standard-Model Extension, including for the first time the coefficient associated with the time-time component of the new field responsible for inducing local Lorentz violation in the theory.

We show that violation of the Lorentz symmetry in quantum electrodynamics can suppress the rates of the interactions crucial for the formation of photon-induced air showers, such as pair production on nuclei and in the geomagnetic field. As a consequence, the allowed region in the space of Lorentz-violating parameters will be seriously restricted if several photons with energies ≥ 10¹⁹ eV are detected.

The KLOE collaboration recently reported bounds on the directional dependence of the lifetime of the short-lived neutral kaon K_S with respect to the cosmic microwave background dipole anisotropy. We interpret their results in a general framework developed to probe Lorentz violation in the weak interaction. In this approach a Lorentz-violating tensor χ^μν is added to the standard propagator of the W boson. We derive the K_S decay rate in a naive tree-level model and calculate the asymmetry for the lifetime. By using the KLOE data the real vector part of χ^μν is found to be smaller than 10⁻². We briefly discuss the theoretical challenges concerning nonleptonic decays.

We present a summary of the first search for Lorentz violation in the top quark sector. This study examined the production and decay process using data collected with the D0 detector at the Fermilab Tevatron Collider. In this process, violation of Lorentz invariance would manifest as a periodic variation in the rate at which events occur. This variation was quantified using the Standard-Model Extension framework, and the first limits were set on some of the coefficients (cQ)_μν33 and (cU)_μν33 parametrizing Lorentz violation in the top quark sector.

We derive a Källén-Lehmann representation for the propagator in two models, one consisting purely of scalars, the other also involving fermions, that couple to a set of constant background coupling coefficients transforming as a symmetric observer Lorentz two-tensor. In particular, we establish the form of the oneparticle poles, which are crucial to define consistently the external states in S-matrix amplitudes.

Recently published data suggest a possible solar influence on some nuclear decay rates, including evidence for an annual variation attributed to the varying Earth-Sun distance. Here, we consider the possibility that the annual signal seen by the DAMA collaboration, and interpreted by them as evidence for dark matter, may in fact be due to the radioactive contaminant ⁴⁰K, which is known to be present in their detector. We also consider the possibility that part of the DAMA signal may arise from relic big-bang neutrinos.

If Lorentz symmetry is broken, it must have occurred dynamically, via a vector or tensor field whose potential energy forces it to take on a nonzero background expectation value ‘in vacuum.’ If the set of minima of this potential (the vacuum manifold) has a nontrivial topology, then there can arise topological defects: stable solutions in which the field approaches different potential minima as we go to infinity in different directions. I discuss the current status of research into these topological defects in the context of Lorentz symmetry breaking, including recent results concerning the birefringent light bending of monopole solutions, and the search for models supporting cosmic-string and domain-wall defects.

We have developed an apparatus to test Lorentz invariance in the photon sector by measuring the resonant frequency difference between two counterpropagating directions of an asymmetric optical ring cavity using a double-pass configuration. No significant evidence for the violation was found at the level of δc/c ≤ 10⁻¹⁴. Details of our apparatus and recent results are presented.

A high performance Space-Time Reference in orbit could be realized using a stable atomic clock in a precisely defined orbit and linking that to high accuracy atomic clocks on the ground using a laser based time-transfer link. This would enhance performance of existing systems and provide unique capabilities in navigation, precise timing, earth sciences, geodesy and the same approach could provide a platform for testing fundamental physics in space. Precise laser timeand frequency-transfer from the ground to an orbiting satellite would make it possible to improve upon the current state of the art in timing (about 1 to 30 ns achieved with GPS) by roughly a factor of 1000 to the 1 ps level.

We analyse the Einstein equivalence principle (EEP) for a Hubble observer in Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We show that the affine structure of the light cone in the FLRW spacetime should be treated locally in terms of the optical metric g_αβ which is not reduced to the Minkowski metric f_αβ due to the nonuniform parametrization of the local equations of light propagation with the proper time of the observer's clock. The physical consequence of this difference is that the Doppler shift of radio waves measured locally is affected by the Hubble expansion.

The unitarity of a Lorentz-invariance violating QED model with higher-order Myers and Pospelov photons coupled to standard fermions is studied. As expected, we find ghost states associated to the higher-order terms that may lead to the loss of unitarity. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to be preserved.

The possible existence of short-range forces between unpolarized and polarized spin- particles has attracted the attention of physicists for decades. These forces are predicted in various theories and provide a possible new source for parity (P) and time reversal (T) symmetry violation. We use an ensemble of polarized ³He gas in a cell with a 250 μm thickness glass window to search for a force from pseudoscalar boson exchange over sub-millimeter ranges. This interaction would produce a nuclear magnetic resonance frequency shift as an unpolarized mass is moved near and far from the polarized ensemble. Recently, we reported a new upper bound with a factor of 10–30 improvement on the product of the scalar coupling to the fermions in the unpolarized mass and the pseudoscalar coupling of the polarized neutron in the ³He nucleus for force ranges from 10⁻⁴ to 10⁻² m, which corresponds to a mass range of 2 × 10⁻³ to 2 × 10⁻⁵ eV for the pseudoscalar boson. This represents the most sensitive published search that sets a direct limit in this important axion window. Currently, a new experiment is being designed and constructed to improve the sensitivity by another factor of 10–100 in the similar region.

The lagrangian-based Standard-Model Extension framework offers a broad description of possible gravitational effects from local Lorentz violation. In this talk, I review the status of the theoretical and phenomenological work in this area. The extension of previous results in linearized gravity to the nonlinear regime is discussed.

Axion-like particles (ALP) are light and weakly interacting pseudoscalars, much studied for solving some technical problems in the Standard Model, and for being viable candidates for dark matter. Direct experimental searches for ALP usually try to detect the interaction with the photon. In a recent work, we pointed out the generation of this coupling as an effect of quantum corrections, originating from an underlying Lorentz violating background. This mechanism depends on the existence of a fermion field which couples to the pseudoscalar and to the photon with specific Lorentz violating interactions. We show that as a consequence of this couplings, the photon effective action contains an ALP-photon interaction that turns out to be Lorentz invariant, thus mimicking the standard coupling studied in current ALP experiments. This consideration shows that violations of spacetime symmetries, much studied as possible consequences of physics in the very high energy scales, might infiltrate in other contexts in unsuspected ways. We thus hope to point out a new connection between theories involving Lorentz violating backgrounds and experiments.

We report on our current progress in the study of finite one-loop radiative corrections in the minimal Lorentz- and CPT-violating QED extension.

The framework of the Standard-Model Extension (SME) provides a relativistic quantum field theory for the study of Lorentz violation. The classical, nonrelativistic equations of motion can be extracted as a limit that is useful in various scenarios. In this work, we consider the effects of certain SME coefficients for Lorentz violation on the motion of macroscopic objects having net intrinsic spin in the classical, nonrelativistic limit.

Searches for new physics often benefit from improved technologies. Here we discuss possible applications of two emerging technologies to searches for physics beyond the Standard Model. First, laser frequency combs enable broad spectral coverage and coherent conversion between optical and RF signals. We are investigating tests of the nonminimal Standard-Model Extension using frequency combs coupled to broadband optical cavities. Second, nitrogen vacancy centers in diamond enable precision nanoscale magnetometry with applications from imaging to quantum science. We are investigating their use in searches for short-range spin-spin couplings.

Our search for nonmagnetic spin-dependent interactions is based on the measurement of free precession of nuclear spin polarized ³He and ¹²⁹Xe atoms in a homogeneous magnetic guiding field of about 400 nT. We report on our approach to perform an adiabatic rotation of the guiding field that allows us to modulate possible nonmagnetic spin-dependent interactions and to find an optimization procedure for long transverse relaxation times T^*₂ both for helium and xenon.

We seek to distinguish and classify relativity theories based on their dispersion relations. Propositions for modified relativity theories can be made by deforming the dispersion relation of Special Relativity. We investigate the critical points of the dispersion relations in order to identify which of these modified dispersion relations represents a change of variables and which represents a significantly different theory.

We present a proposal to include Lorentz-violating effects in a gravitational field by means of Finsler geometry. In the Finsler setup, the length of an event depends both on the point and the direction in the spacetime. We briefly review the bumblebee model, where the Lorentz violation is induced by a spontaneous symmetry breaking due to the bumblebee vector field. The main geometrical concepts of Finsler geometry are outlined. Using a finslerian Einstein-Hilbert action we derive the bumblebee action from the bipartite Finsler function with a correction to the gravitational constant.

The use of microlocal analysis is considered in proving renormalizability of a particular minimal SME model, as well as of a model of scalar tachyons.

Radiative corrections in quantum field theories with small departures from Lorentz symmetry alter structural aspects of the theory, in particular the definition of asymptotic single-particle states. Specifically, the Dirac equation is radiatively modified by Lorentz-violating momentum-dependent operators not present in the Lagrange density, and the standard renormalization procedure needs to be adapted too.

Preliminary data from improvements made in our experimental setup are presented. Forces measured with our setup are presented and possible origins for the systematics observed are discussed. The observed signal is most likely induced by an impulsive oscillation of the motor.

In this short review we describe a recently proposed model of gravity with spontaneously broken Lorentz invariance, with massless gravitons as Nambu-Goldstone modes. Interactions follow from imposing consistent coupling to the total energy-momentum tensor. At low energies the Einstein-Hilbert action is reproduced.

We have analyzed Maxwell-Chern-Simons-Higgs BPS vortices in a Lorentz-violating CPT-odd context. The Lorentz violation induces profiles with a conical behavior at the origin. For some combination of the coefficients for Lorentz violation there always exists a sufficiently large winding number for which the magnetic field flips its sign.

A frequently confused point in studies of symmetry violation is the distinction between observer and particle transformations. In this work, we consider a model in which a coefficient in the Standard-Model Extension leads to violations of rotation invariance in Newton's second law. The model highlights the distinction between observer and particle transformations.